A common goal in game theory is to determine the existence of equilibrium points, i.e. profiles that in some way represent a satisfactory choice for both players [1]}. The most famous equilibrium notion is due to Nash. Intuitively, a profile is a Nash equilibrium if each player does not have any interest in changing his choice assuming the other does not change his strategy. For the particular case of a 2-player game, a profile \((z_{1,i^*}, z_{2,j^*})\)  is a Nash equilibrium if:
\(\begin{array}{ll}v_1((z_{1,i^*}, z_{2,j^*})) \ge v_1((z_{1,i}, z_{2,j^*})) & \forall z_{1,i} \in \mathcal {S}_1\\v_2((z_{1,i^*}, z_{2,j^*})) \ge v_2((z_{1,i^*}, z_{2,j})) & \forall z_{2,j} \in \mathcal {S}_2,\end{array}\) 
